There is quite some overlap with fan fiction, because people like to "fix" non-rational fiction. Eliezer Yudkowsky and his take on Harry Potter is the prime example. I can also recommend Alexander Wales who also made original fiction.

Probably the oldest related work is A Connecticut Yankee in King Arthur's Court by Mark Twain.

Another name mentioned often in this genre is Brandon Sanderson and especially his Mistborn series, but I have not read it personally.